Abstract Algebra - A PID That Is Not a Euclidean Domain

Explore an advanced topic in abstract algebra through this 37-minute video lecture that presents an example of a principal ideal domain (PID) that is not a Euclidean domain. Follow the outline described in Dummit and Foote to learn that an integral domain D is a PID if and only if it has a Dedekind-Hasse Norm, and that every Euclidean domain has a universal side divisor. Discover how the presented example has a Dedekind-Hasse norm but no universal side divisor, demonstrating the distinction between PIDs and Euclidean domains. Gain insights into this complex mathematical concept as explained by Michael Penn, enhancing your understanding of abstract algebra and ideal theory.